Question

A geneticist grows 15 pea plants for each experiment. Assume that he has carried out an infinite number of experiments and measured the mean height of the plants each time. He finds that the population mean of the plant heights is 6.5 feet with a standard deviation of 0.5 feet. In what interval will 95% of the sample means occur?
the options are
a. 6.47 & 6.53 feet
b. 6.37 & 6.63 feet
c. 6.35 & 6.65 feet
d. 6.24 & 6.76 feet

Answer 1

With beginner statistics, you have learned about the 68-95-99.7 rule. As the picture shows, the standard deviation shows how the height of the plants would vary from the population mean.

You see as the heights move one standard deviation away from the right and left of the peak, 68% of plants sampled would have the height between 6 to 7 feet.

Now for one more step, to include 95% of samples you would add two standard deviations away. Therefore you would add 1 feet higher and lower to the population mean.

=95% of the samples would have the height between 5.5 feet to 7.5 feet. 

Hope that helped! I love statistics so if you'd like me to go into more detail over the 68-95-99.7 rule

Answer 2

Answer:

D. 6.24 & 6.76

Step-by-step explanation:

The interval for 95% of the sample means is given by,  µ ± $\frac{σ}{\sqrt{n} }$ where µ is the population mean, σ is the standard deviation, and n is the sample size.